Which of the following correctly describes the time value of money?

Question

BlackTom AI · Accepted Answer

Because money can earn interest, a dollar today is worth more than a dollar received one year from today.

1. Relevant knowledge points and concepts
- Time value of money (TVM): money available now can be invested to earn a return, so present funds have higher value than identical nominal amounts received in the future.
- Opportunity cost: receiving money later prevents you from using it for consumption or investment now.
- Present value (PV) and future value (FV) relationship: FV = PV × (1 + r)^n and PV = FV / (1 + r)^n, where r is the interest rate and n is the number of periods.
- Inflation and risk reduce future purchasing power, reinforcing TVM.

2. Step-by-step reasoning
- Start from the principle that if you have $1 today you can invest it at a market interest rate r, so after one year it becomes $1 × (1 + r).
- Conversely, one dollar promised in one year must be discounted back to today by dividing by (1 + r) to get its present value.
- If r > 0, then PV of $1 in one year = 1 / (1 + r) < 1, so the dollar today is worth more.

3. Calculations with intermediate steps
- Example: assume r = 5% (0.05). FV of $1 today after one year = 1 × (1 + 0.05) = $1.05.
- PV of $1 received in one year = 1 / (1 + 0.05) = 1 / 1.05 = 0.95238095 ≈ $0.9524 today.
- Since $1.00 today > $0.9524, a dollar today is worth more than a dollar in a year.

4. Why the correct answer is correct
- The correct option states that "A dollar today is worth more than a dollar received one year from today," which directly reflects the TVM principle and the mathematical PV/FV relationship when interest rates are positive. It captures opportunity cost, potential investment returns, and inflation effects.

5. Why the other options are incorrect
- "A dollar today is worth less than a dollar received one year from today": incorrect because it ignores the ability to invest today’s dollar and earn returns.
- "The value of a dollar does not change over time": incorrect because interest rates, inflation, and opportunity costs change the real and nominal value over time.
- "The time value of money applies only to international transactions": incorrect because TVM is a fundamental financial concept that applies to all transactions, domestic and international.

6. Conclusion
The correct answer is "A dollar today is worth more than a dollar received one year from today," which matches the provided answer.

Which of the following correctly describes the time value of money?Single choice

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